The de Sitter swampland conjecture and supersymmetric AdS vacua

TL;DR

This paper explores the connection between the de Sitter swampland conjecture and the absence of supersymmetric AdS vacua, showing their equivalence in certain string theory models and implications for potential positivity.

Contribution

It demonstrates that the de Sitter swampland conjecture is equivalent to the absence of supersymmetric Minkowski or AdS solutions in several string models, clarifying their relationship.

Findings

The conjecture implies potential positivity at large radius.

It is incompatible with the simplest KKLT AdS supersymmetric solution.

Establishes an equivalence between the conjecture and absence of certain supersymmetric vacua.

Abstract

It has recently been conjectured that string theory does not admit de Sitter critical points. This note points out that in several cases, including KKLT or racetrack models, this statement is equivalent to the absence of supersymmetric Minkowski or AdS solutions. This equivalence arises from establishing the positivity of the potential in a large-radius limit, requiring a turnover of the potential before reaching an AdS vacuum. For example, this conjecture is incompatible with the simplest 1-modulus KKLT AdS supersymmetric solution.